2022/06/22 by Max Heldman, Heldman, Max, Samuel A. Isaacson +5
Mathematics · Medicine · #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Statistical Methods and Bayesian Inference #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2206.10819
openalex publication_date 2022/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recent works have derived and proven the large-population mean-field limit for several classes of particle-based stochastic reaction-diffusion (PBSRD) models. These limits correspond to systems of partial integral-differential equations (PIDEs) that generalize standard mass-action reaction-diffusion PDE models. In this work we derive and prove the next order fluctuation corrections to such limits, which we show satisfy systems of stochastic PIDEs with Gaussian noise. Numerical examples are presented to illustrate how including the fluctuation corrections can enable the accurate estimation of higher order statistics of the underlying PBSRD model.